观察下列三行数:-1,2,-4,8,-16,32,…; ①-2,4,-8,16,-32,64,…;
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观察下列三行数:
-1,2,-4,8,-16,32,…; ①
-2,4,-8,16,-32,64,…; ②
0,6,-6,18,-30,66,…; ③
(1)第①行数按什么规律排列?
(2)第②③行数与第①行数分别有什么关系?
(3)取每行数的第n个数,这三个数的和能否等于-1278?如果能,指出是每行的第几个数,并求出这三个数;如果不能,请说明理由.
-1,2,-4,8,-16,32,…; ①
-2,4,-8,16,-32,64,…; ②
0,6,-6,18,-30,66,…; ③
(1)第①行数按什么规律排列?
(2)第②③行数与第①行数分别有什么关系?
(3)取每行数的第n个数,这三个数的和能否等于-1278?如果能,指出是每行的第几个数,并求出这三个数;如果不能,请说明理由.
![观察下列三行数:-1,2,-4,8,-16,32,…; ①-2,4,-8,16,-32,64,…;](/uploads/image/z/71454-30-4.jpg?t=%E8%A7%82%E5%AF%9F%E4%B8%8B%E5%88%97%E4%B8%89%E8%A1%8C%E6%95%B0%EF%BC%9A-1%EF%BC%8C2%EF%BC%8C-4%EF%BC%8C8%EF%BC%8C-16%EF%BC%8C32%EF%BC%8C%E2%80%A6%EF%BC%9B%26nbsp%3B%E2%91%A0-2%EF%BC%8C4%EF%BC%8C-8%EF%BC%8C16%EF%BC%8C-32%EF%BC%8C64%EF%BC%8C%E2%80%A6%EF%BC%9B%26nbsp%3B)
(1)∵-1,2,-4,8,-16,32,…,
∴第n个数为(-1)n•2n-1;
(2)第②行的数为第①行相应的数的2倍,2(-1)n•2n-1=(-1)n•2n,
第③行的数为第②行相应的数加2,(-1)n•2n+2;
(3)∵三行的相应的数的正负情况相同,
∴-2n-1-2n-2n+2=-1278,
整理得,2n=512,
解得n=9,
三个数分别为:(-1)9•29-1=-256,
(-1)9•29=-512,
(-1)9•29+2=-512+2=-510.
∴第n个数为(-1)n•2n-1;
(2)第②行的数为第①行相应的数的2倍,2(-1)n•2n-1=(-1)n•2n,
第③行的数为第②行相应的数加2,(-1)n•2n+2;
(3)∵三行的相应的数的正负情况相同,
∴-2n-1-2n-2n+2=-1278,
整理得,2n=512,
解得n=9,
三个数分别为:(-1)9•29-1=-256,
(-1)9•29=-512,
(-1)9•29+2=-512+2=-510.
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